It is "extraordinarily difficult to find a statistician who argues explicitly in favor of the retention of significance tests...." (Oakes, 1986)

Notwithstanding that statement,

"Null hypothesis testing is insufficient when size of effect is important, but it is ideal for testing "ordinal" claims relating the order of conditions, which are common in psychology. Null hypothesis testing also is insufficient for determining beliefs, but it is ideal for demonstrating sufficient evidential strength to support an ordinal claim, with sufficient evidence being one criterion for a finding entering the corpus of legitimate findings in psychology. The line between sufficient and insufficient evidence is currently set at p < .05; there is little reason for allowing experimenters to select their own value of alpha. Thus, null hypothesis testing is an optimal method for demonstrating sufficient evidence for an ordinal claim." (Frick, 1996)